JEE Main 2024 (Online) 30th January Morning ShiftQuestion 1
A line passing through the point $A(9,0)$ makes an angle of $30^{\circ}$ with the positive direction of $x$-axis. If this line is rotated about $A$ through an angle of $15^{\circ}$ in the clockwise direction, then its equation in the new position is :
Points and Straight Lines
Solution
Original slope $\tan30^\circ$; rotating clockwise by $15^\circ$ gives inclination $15^\circ$, slope $\tan15^\circ=2-\sqrt3$. Line: $y=(2-\sqrt3)(x-9)\Rightarrow \frac{y}{2-\sqrt3}=x-9\Rightarrow x-\frac{y}{2-\sqrt3}=9\Rightarrow \frac{y}{\sqrt3-2}+x=9$. Answer (A).